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Title: Effective medium theory of random regular networks
Abstract Disordered spring networks can exhibit rigidity transitions, due to either the removal of material in over-constrained networks or the application of strain in under-constrained ones. While an effective medium theory (EMT) exists for the former, there is none for the latter. We, therefore, formulate an EMT for random regular, under-constrained spring networks with purely geometrical disorder to predict their stiffness via the distribution of tensions. We find a linear dependence of stiffness on strain in the rigid phase and a nontrivial dependence on both the mean and standard deviation of the tension distribution. While EMT does not yield highly accurate predictions of shear modulus due to spatial heterogeneities, it requires only the distribution of tensions for an intact system, therefore making it an ideal starting point for experimentalists quantifying the mechanics of such networks.  more » « less
Award ID(s):
1951921
PAR ID:
10430035
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Europhysics Letters
Volume:
138
Issue:
2
ISSN:
0295-5075
Page Range / eLocation ID:
27001
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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